The Extension of Isometry between Unit Spheres of Normed Space $E$ and $l^1$
Received:July 27, 2007  Revised:April 16, 2008
Key Word: isometry   surjective   linearly isometric extension.
Fund ProjectL:the National Natural Science Foundation of China (No.10571090); the Research Fund for the Doctoral Program of Higher Education (No.20060055010) and the Fund of Tianjin Educational Comittee (No.20060402).
 Author Name Affiliation ZHAN Hua Ying College of Science, Tianjin University of Technology, Tianjin 300384, China
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The main result of this paper is to prove Fang and Wang's result by another method: Let $E$ be any normed linear space and $V_0: S(E)\rightarrow S(l^1)$ be a surjective isometry. Then $V_0$ can be linearly isometrically extended to $E$.